Think of it like a bucket of 100 for every 30 seconds. The first 50 messages in the bucket can be sent to any of the channels, 51-100 can only be sent to the channels where the bot has mod status.
You must trust the broadcasters in order to use the 51-100. If the bot gets unmodded between messages 51 and 52, for example, there is no way for the bot to detect this in time and the 52nd message will exceed the rate limit. Multichannel bots should always stick to the known/verified bot limit for this reason.